Math 1101 Exam 2 Practice Problems
These problems are not intended to cover all possible test topics. These problems should serve
as an activity in preparing for your test, but other study is required to fully prepare. These problems
contain some multiple choice questions, please consult with your instructor for particular details
about your class test.
1. Determine if the graph of the function y = x2 − 4x + 4 is concave up or concave down.
A. Concave down
B. Concave up
2. Determine if the vertex of the graph of f (x) = −4x2 + 2x − 5 is a maximum point or a
minimum point.
A. Minimum
B. Maximum
3. Give the coordinates of the vertex.
(a) y = x2 + 2x + 3
A. Vertex: (−1, 2)
B. Vertex: (1, 2)
C. Vertex: (−1, −4)
(b) y = (x + 8)2 − 9
A. Vertex: (−8, 9)
B. Vertex: (8, 9)
C. Vertex: (8, −9)
D. Vertex: (1, 4)
D. Vertex: (−8, −9)
4. Use the graph of the function y = x2 + 3x − 18 to estimate the x-intercepts.
A. x = 0
B. x = −6, x = 3
C. x = −3, x = 18
D. x = −3, x = 6
5. John owns a hot dog stand. He has found that his profit is given by the equation P = −x2 +
54x + 75, where x is the number of hot dogs sold. How many hot dogs must he sell to earn
the most profit? A. 24 hot dogs B. 48 hot dogs C. 28 hot dogs D. 27 hot dogs
6. Use factoring to solve the equation
3x2 − 15x + 18 = 0
Solution:
3x2 − 15x + 18 = 0
3(x2 − 5x + 6) = 0
3(x − 3)(x − 2) = 0
Either x − 3 = 0 or x − 2 = 0, yielding x = 3 or x = 2.
MATH 1101
Exam 2 Review, Page 2 of 7
Fall 2013
7. Find the x-intercepts of y = 4x2 − 6x.
Solution: The x-intercepts occur when y = 0:
0 = 4x2 − 6x
0 = 2x(2x − 3)
Either 2x = 0 or 2x − 3 = 0, yielding x = 0 or x = 3/2.
8. Use the quadratic formula to solve the equation p2 + 5p − 5 = 0.
√
√
√
√
−5 ± 3 5
−5 − 3 5
5+3 5
A.
B.
C. −5 ± 3 5 D.
2
2
2
9. Use a graphing utility to find or approximate solutions 4n2 = −6n − 1. If necessary, round
your answers to three decimal places.
A. −0.191, −1.309
B. −0.941, −2.059
C. 0.151, −1.651
D. −0.095, −0.655
10. A ball is thrown downward from a window in a tall building. The distance traveled by the ball
in t seconds is s = 16t2 + 32t, where s is in feet. how long (to the nearest tenth) will it take
the ball to fall 96 feet?
A. 2.6 sec
B. 2.4 sec
C. 1.4 sec
D. 1.6 sec
11. Graph without the use of technology.
1
(a) f (x) = − 4
x
√
(b) y = x − 2
12. Find f (6) for


3x + 1,
f (x) = 6x,


6 − 6x,
A. −30
B. 4
C. 36
if x < 1;
if 6 ≤ x ≤ 9;
if x > 9.
D. 55
4
13. Determine if the function y = x 3 is concave up or concave down in the first quadrant.
A. Concave up B. Concave down
14. Determine if the function y = −3x4 is increasing or decreasing for x < 0 by drawing a sketch
of the graph using your knowledge of the graph of the power function y = x4 .
A. Increasing
B. Decreasing
MATH 1101
Exam 2 Review, Page 3 of 7
Fall 2013
15. The graph of y = −5(x − 4)2 + 7 can be obtained from the graph of y = x2 by shifting horiunits to the
, vertically stretching by a factor of
,
zontally
reflecting across the
-axis, and shifting vertically
units in the
direction.
Solution: The graph of y = −5(x − 4)2 + 7 can be obtained from the graph of y = x2
by shifting horizontally 4 units to the right, vertically stretching by a factor of 5, reflecting
across the x-axis, and shifting vertically 7 units in the upward direction.
16. Write the equation of the graph after the indicated transformations: The graph of y =
shifted 2 units to the left. Then the graph is shifted 3 units upward.
√
√
√
√
A. y = x + 3 + 2 B. y = x − 2 + 3 C. y = x + 2 + 3 D. y = 3 x + 2
√
x is
17. Determine whether the graph of f (x) = −8x3 + 4x is symmetric with respect to the x-axis,
the y-axis, and/or the origin.
Solution:
f (−x) = −8(−x)3 + 4(−x) = 8x3 − 4x = −f (x)
So the graph of f (x) is symmetric with respect to the origin.
18. Determine whether the function y =
A. Odd
B. Even
√
x2 + 3 is even, odd, or neither.
C. Neither
19. A furniture manufacturer decides to make a new line of desks. The table shows the profit, in
thousands of dollars, for various levels of production.
Number of Desks Produced 120
Profit (thousands)
13
350
37
500
44
650
34
750
25
Find a quadratic function that best fits the data, and use the model to predict the profit if 450
desks are made.
A. Almost $44,000
B. Almost $42,000
C. Just over $40,000
D. Just under $45,000
MATH 1101
Exam 2 Review, Page 4 of 7
Fall 2013
20. The percent of people who say they plan to stay in the same job position until they retire has
decreased over recent years, as shown in the table below.
Year
1995
Percent 42
1996
38
1997
35
1998
34
1999
30
2000
26
Find a power function that models the data in the table using an input equal to the number of
years from 1990.
A. y = 43.934x−0.240
B. y = −0.638x120.077
C. y = 52.857x−0.071
D. y = 120.077x−0.638
21. The following table has the inputs x and the outputs for three functions f , g, and h. Use
second differences to determine which function is exactly quadratic, which is approximately
quadratic, and which is not quadratic.
x f (x) g(x) h(x)
6
0
0
0
1 6.4
0.8
2.9
3.2 12.3
2 6.8
3 7.2
7.2 26.8
4 7.6 12.8 47.4
8
20 75.2
5
Solution:
x f (x)
0
6
1 6.4
2 6.8
3 7.2
4 7.6
5
8
1st diff 2nd diff
0.4
0.4
0.4
0.4
0.4
0
0
0
0
The first differences of f (x) are constant hence is exactly linear, so it is not quadratic.
x
0
1
2
3
4
5
g(x)
0
0.8
3.2
7.2
12.8
20
1st diff 2nd diff
0.8
2.4
4
5.6
7.2
1.6
1.6
1.6
1.6
The second differences of g(x) are constant, hence it is exactly quadratic.
MATH 1101
x
0
1
2
3
4
5
Exam 2 Review, Page 5 of 7
Fall 2013
h(x) 1st diff 2nd diff
0
2.9
2.9
12.3
9.4
6.5
26.8
14.5
5.1
47.4
20.6
6.1
75.2
27.8
7.2
The second differences of h(x) are approximately constant, hence it is approximately
quadratic.
22. Determine whether a linear or quadratic function would be a more appropriate model for the
graphed data. If linear, tell whether the slope should be positive or negative. If quadratic,
decide whether the coefficient of x2 should be positive or negative.
A. Linear; positive
positive
B. Quadratic; negative
C. Linear; negative
√
23. For f (x) = 2x − 5 and g(x) = x + 9, what is the domain of
A. [0, ∞)
B. [9, ∞)
C. (−9, 9)
D. (−9, ∞)
f
(x)?
g
D. Quadratic;
MATH 1101
Exam 2 Review, Page 6 of 7
Fall 2013
24. Given f (x) = 4x2 + 6x + 7 and g(x) = 6x − 8, find (g ◦ f )(x).
Solution:
(g ◦ f )(x) = g(f (x))
= g(4x2 + 6x + 7)
= 6(4x2 + 6x + 7) − 8
= 24x2 + 36x + 42 − 8
= 24x2 + 36x + 34
25. Find (g ◦ f )(−4) when f (x) = 4x + 5 and g(x) = 4x2 − 5x − 3.
A. 9
B. 536
C. 329
D. 8
26. Use the graphs of f and g to find (g ◦ f )(−3).
(a) y = f (x)
(b) y = g(x)
Solution:
(g ◦ f )(−3) = g(f (−3))
= g(−2)
=3
MATH 1101
Exam 2 Review, Page 7 of 7
Fall 2013
27. At Allied Electronics, production has begun on the X-15 Computer Chip. The total revenue
function is given by R(x) = 60x − 0.3x2 and the total cost function is given by C(x) =
10x + 12, where x represents the number of boxes of computer chips produced. The total
profit function, P (x), is such that P (x) = R(x) − C(x). Find P (x).
A. P (x) = −0.3x2 + 50x − 12
B. P (x) = 0.3x2 + 50x − 24
C. P (x) = 0.3x2 + 40x − 36
D. P (x) = −0.3x2 + 40x + 12